Noncommutative field theories has been studied extensively in the previous two decades [1]}, [2]}, [3]}, [4]}, [5]}, [6]}. The noncommutativity appears naturally in quantum mechanics when we study the motion of a charged particle moving in two-dimensions under the presence of a constant, perpendicular magnetic field[2]}, [8]} and more broadly in the context of quantum Hall effect[9]}, [10]}, [11]}. Other studies suggest the appearance of non-commutativity in the study of open string field theory in the presence of \(B\) -field[12]}, [13]}, [14]}, [15]}. Very recently, a possible application in the emerging field of magnetic skyrmions has been reported [16]}, [17]}, [18]}
